html, body, form { margin: 0; padding: 0; width: 100%; } #calculate { position: relative; width: 177px; height: 110px; background: transparent url(/images/alphabox/embed_functions_inside.gif) no-repeat scroll 0 0; } #i { position: relative; left: 18px; top: 44px; width: 133px; border: 0 none; outline: 0; font-size: 10px; } #eq { width: 9px; height: 10px; background: transparent; position: absolute; top: 47px; right: 18px; cursor: pointer; }

 ArcCosh

 http://functions.wolfram.com/01.26.16.0159.01

 Input Form

 ArcCosh[x] - ArcCosh[y] == ArcSinh[ (-1)^Floor[1/2 - Arg[(-x) y + Sqrt[-1 + x] Sqrt[1 + x] Sqrt[-1 + y] Sqrt[1 + y]]/Pi] ((-Sqrt[-1 + x]) Sqrt[1 + x] y + x Sqrt[-1 + y] Sqrt[1 + y])] + (1/2) Pi ((((1/2) I)/(-1)^Floor[-(Arg[1 - x]/(2 Pi))] + ((1/2) I)/(-1)^Floor[-(Arg[1 - y]/(2 Pi))]) (-1 + (-1)^Floor[1/2 - Arg[x y + Sqrt[1 - x^2] Sqrt[1 - y^2]]/Pi] + 2 (-1 + (-1)^Floor[1/2 - Arg[x y + Sqrt[1 - x^2] Sqrt[1 - y^2]]/Pi]) Floor[(Arg[I x + Sqrt[1 - x^2]] + Arg[(-I) y + Sqrt[1 - y^2]])/ (2 Pi)] + 2 (1 + (-1)^Floor[1/2 - Arg[x y + Sqrt[1 - x^2] Sqrt[1 - y^2]]/Pi]) Floor[1/2 - (Arg[I x + Sqrt[1 - x^2]] + Arg[(-I) y + Sqrt[1 - y^2]])/ (2 Pi)]) + (((1/2) I)/(-1)^Floor[-(Arg[1 - x]/(2 Pi))] - ((1/2) I)/(-1)^Floor[-(Arg[1 - y]/(2 Pi))]) (1 + (-1)^Floor[1/2 - Arg[(-x) y + Sqrt[1 - x^2] Sqrt[1 - y^2]]/Pi] + 2 (-1 + (-1)^Floor[1/2 - Arg[(-x) y + Sqrt[1 - x^2] Sqrt[1 - y^2]]/Pi]) Floor[(Arg[I x + Sqrt[1 - x^2]] + Arg[I y + Sqrt[1 - y^2]])/(2 Pi)] + 2 (1 + (-1)^Floor[1/2 - Arg[(-x) y + Sqrt[1 - x^2] Sqrt[1 - y^2]]/Pi]) Floor[1/2 - (Arg[I x + Sqrt[1 - x^2]] + Arg[I y + Sqrt[1 - y^2]])/ (2 Pi)]))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcCosh", "[", "x", "]"]], "-", RowBox[List["ArcCosh", "[", "y", "]"]]]], "\[Equal]", RowBox[List[RowBox[List["ArcSinh", "[", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["Floor", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[RowBox[List["Arg", "[", RowBox[List[RowBox[List[RowBox[List["-", "x"]], " ", "y"]], "+", RowBox[List[SqrtBox[RowBox[List[RowBox[List["-", "1"]], "+", "x"]]], " ", SqrtBox[RowBox[List["1", "+", "x"]]], " ", SqrtBox[RowBox[List[RowBox[List["-", "1"]], "+", "y"]]], " ", SqrtBox[RowBox[List["1", "+", "y"]]]]]]], "]"]], "\[Pi]"]]], "]"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", SqrtBox[RowBox[List[RowBox[List["-", "1"]], "+", "x"]]]]], " ", SqrtBox[RowBox[List["1", "+", "x"]]], " ", "y"]], "+", RowBox[List["x", " ", SqrtBox[RowBox[List[RowBox[List["-", "1"]], "+", "y"]]], " ", SqrtBox[RowBox[List["1", "+", "y"]]]]]]], ")"]]]], "]"]], "+", 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"2"]]]]]], "]"]]]], RowBox[List["2", " ", "\[Pi]"]]], "]"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["1", "+", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["Floor", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[RowBox[List["Arg", "[", RowBox[List[RowBox[List[RowBox[List["-", "x"]], " ", "y"]], "+", RowBox[List[SqrtBox[RowBox[List["1", "-", SuperscriptBox["x", "2"]]]], " ", SqrtBox[RowBox[List["1", "-", SuperscriptBox["y", "2"]]]]]]]], "]"]], "\[Pi]"]]], "]"]]]]], ")"]], " ", RowBox[List["Floor", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[RowBox[List[RowBox[List["Arg", "[", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "x"]], "+", SqrtBox[RowBox[List["1", "-", SuperscriptBox["x", "2"]]]]]], "]"]], "+", RowBox[List["Arg", "[", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "y"]], "+", SqrtBox[RowBox[List["1", "-", SuperscriptBox["y", "2"]]]]]], "]"]]]], RowBox[List["2", " ", "\[Pi]"]]]]], "]"]]]]]], ")"]]]]]], ")"]]]]]]]]]]

 MathML Form

 cosh - 1 ( x ) - cosh - 1 ( y ) sinh - 1 ( ( - 1 ) 1 2 - arg ( x - 1 x + 1 y - 1 y + 1 - x y ) π ( x y - 1 y + 1 - x - 1 x + 1 y ) ) + 1 2 π ( ( 1 2 ( - 1 ) - - arg ( 1 - x ) 2 π + 1 2 ( - 1 ) - - arg ( 1 - y ) 2 π ) ( 2 ( - 1 + ( - 1 ) 1 2 - arg ( x y + 1 - x 2 1 - y 2 ) π ) arg ( x + 1 - x 2 ) + arg ( 1 - y 2 - y ) 2 π + ( - 1 ) 1 2 - arg ( x y + 1 - x 2 1 - y 2 ) π + 2 ( 1 + ( - 1 ) 1 2 - arg ( x y + 1 - x 2 1 - y 2 ) π ) 1 2 - arg ( x + 1 - x 2 ) + arg ( 1 - y 2 - y ) 2 π - 1 ) + ( 1 2 ( - 1 ) - - arg ( 1 - x ) 2 π - 1 2 ( - 1 ) - - arg ( 1 - y ) 2 π ) ( 2 ( - 1 + ( - 1 ) 1 2 - arg ( 1 - x 2 1 - y 2 - x y ) π ) arg ( x + 1 - x 2 ) + arg ( y + 1 - y 2 ) 2 π + ( - 1 ) 1 2 - arg ( 1 - x 2 1 - y 2 - x y ) π + 2 ( 1 + ( - 1 ) 1 2 - arg ( 1 - x 2 1 - y 2 - x y ) π ) 1 2 - arg ( x + 1 - x 2 ) + arg ( y + 1 - y 2 ) 2 π + 1 ) ) x -1 y -1 1 2 -1 x -1 1 2 x 1 1 2 y -1 1 2 y 1 1 2 -1 x y -1 x y -1 1 2 y 1 1 2 -1 x -1 1 2 x 1 1 2 y 1 2 1 2 -1 -1 -1 1 -1 x 2 -1 1 2 -1 -1 -1 1 -1 y 2 -1 2 -1 -1 1 2 -1 x y 1 -1 x 2 1 2 1 -1 y 2 1 2 -1 x 1 -1 x 2 1 2 1 -1 y 2 1 2 -1 y 2 -1 -1 1 2 -1 x y 1 -1 x 2 1 2 1 -1 y 2 1 2 -1 2 1 -1 1 2 -1 x y 1 -1 x 2 1 2 1 -1 y 2 1 2 -1 1 2 -1 x 1 -1 x 2 1 2 1 -1 y 2 1 2 -1 y 2 -1 -1 1 2 -1 -1 -1 1 -1 x 2 -1 -1 1 2 -1 -1 -1 1 -1 y 2 -1 2 -1 -1 1 2 -1 1 -1 x 2 1 2 1 -1 y 2 1 2 -1 x y -1 x 1 -1 x 2 1 2 y 1 -1 y 2 1 2 2 -1 -1 1 2 -1 1 -1 x 2 1 2 1 -1 y 2 1 2 -1 x y -1 2 1 -1 1 2 -1 1 -1 x 2 1 2 1 -1 y 2 1 2 -1 x y -1 1 2 -1 x 1 -1 x 2 1 2 y 1 -1 y 2 1 2 2 -1 1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["ArcCosh", "[", "x_", "]"]], "-", RowBox[List["ArcCosh", "[", "y_", "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["ArcSinh", "[", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["Floor", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[RowBox[List["Arg", "[", RowBox[List[RowBox[List[RowBox[List["-", "x"]], " ", "y"]], "+", RowBox[List[SqrtBox[RowBox[List[RowBox[List["-", "1"]], "+", "x"]]], " ", SqrtBox[RowBox[List["1", "+", "x"]]], " ", SqrtBox[RowBox[List[RowBox[List["-", "1"]], "+", "y"]]], " ", SqrtBox[RowBox[List["1", "+", "y"]]]]]]], "]"]], "\[Pi]"]]], "]"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", SqrtBox[RowBox[List[RowBox[List["-", "1"]], "+", "x"]]]]], " ", SqrtBox[RowBox[List["1", "+", "x"]]], " ", "y"]], "+", RowBox[List["x", " ", SqrtBox[RowBox[List[RowBox[List["-", "1"]], "+", "y"]]], " ", 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 Date Added to functions.wolfram.com (modification date)

 2007-05-02